Dynamic modeling of enzyme controlled metabolic networks using a receding time horizon

TL;DR

This paper extends the dynamic enzyme-cost Flux Balance Analysis (deFBA) by including storage and maintenance costs, and introduces a receding horizon approach called sdeFBA, enabling better control and prediction of metabolic networks.

Contribution

It introduces the sdeFBA method using receding horizons in deFBA, providing a systematic way to select horizons and ensure exponential growth conditions.

Findings

sdeFBA effectively models dynamic metabolic processes

Receding horizon improves control and prediction accuracy

Systematic horizon selection enhances solution growth

Abstract

Microorganisms have developed complex regulatory features controlling their reaction and internal adaptation to changing environments. When modeling these organisms we usually do not have full understanding of the regulation and rely on substituting it with an optimization problem using a biologically reasonable objective function. The resulting constraint-based methods like the Flux Balance Analysis (FBA) and Resource Balance Analysis (RBA) have proven to be powerful tools to predict growth rates, by-products, and pathway usage for fixed environments. In this work, we focus on the dynamic enzyme-cost Flux Balance Analysis (deFBA), which models the environment, biomass products, and their composition dynamically and contains reaction rate constraints based on enzyme capacity. We extend the original deFBA formalism to include storage molecules and biomass-related maintenance costs. Furthermore, we present a novel usage of the receding prediction horizon as used in Model Predictive Control (MPC) in the deFBA framework, which we call the short-term deFBA (sdeFBA). This way we eliminate some mathematical artifacts arising from the formulation as an optimization problem and gain access to new applications in MPC schemes. A major contribution of this paper is also a systematic approach for choosing the prediction horizon and identifying conditions to ensure solutions grow exponentially. We showcase the effects of using the sdeFBA with different horizons through a numerical example.